1 Yes, you can use the articles in the way you say, but not in all contexts. We often use possessive adjectives and, to me, it would sound wrong to go to the doctor and say that I had hurt 'the neck'.
2 Hair is usually uncoutable, but a strand of hair can also be called 'a hair.' With Elvis, 'the hair' implies to me that you have all of his hair, so I'd use some of or a lock of Elvis' hair.
3 With naming, the definite article makes sense. The indefinite atrticle would work when the body is not identified (police found a body in the house).
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